In this paper, we present a study of the Sommerfeld effect (Jump phenomena) in a nonideal mechanical oscillator, composed of an unbalanced DC motor, with limited power supply, coupled to the free end of cantilever beam and a shape memory alloy (SMA) actuator that works to damp the vibration. A nonlinear mathematical model for this system is developed. The SMA wire constitutive model considers a nonlinear phase transformation model. Numerical simulations shows the different aspects about the Sommerfeld effect, illustrating the influence of the different temperatures of the SMA actuator on the dynamic of the nonideal system. Keywords: Nonideal oscillator, Shape memory alloy, Jump phenomena